Optimize segment tree operations by inlining method calls

[shakayami]

Summary

This PR optimizes the lazy segment tree and segment tree implementations by inlining frequently called methods and caching instance attributes as local variables. This reduces method call overhead and improves cache locality, resulting in better performance for tree operations.

Key Changes

lazysegtree.py:

• Inlined push() method calls throughout all methods (set, get, prod, apply_point, apply, max_right, min_left) by directly expanding the push logic inline
• Inlined update() method calls by directly computing d[k] = op(d[2*k], d[2*k+1])
• Inlined all_apply() method calls in the apply() method
• Cached instance attributes (d, lz, mapping, composition, identity, op, size, log) as local variables at the start of each method to reduce attribute lookup overhead

segtree.py:

• Inlined update() method calls by directly computing d[k] = op(d[2*k], d[2*k+1])
• Cached instance attributes (d, op, size) as local variables in methods that use them frequently (__init__, set, prod, max_right, min_left)

Implementation Details

• The inlining of push() in lazy segment tree methods eliminates repeated method call overhead while maintaining the same logic
• Local variable caching reduces the cost of attribute lookups (e.g., self.d → d) which is particularly beneficial in tight loops
• All functional behavior remains identical; this is purely a performance optimization
• The changes make the code more verbose but significantly faster for operations on large trees

https://claude.ai/code/session_01MhJ83qTzfEG4xQBrHgRTgY

[github-actions]

📊 Performance Benchmark Results

⏱️ Execution time (mean, lower is better)

Benchmark	Base	PR	Delta
acl_math	2.006s	2.009s	+0.1%
acl_string	241.78ms	242.04ms	+0.1%
convolution	870.59ms	888.54ms	+2.1%
dsu	672.12ms	680.93ms	+1.3%
fenwicktree	1.116s	1.138s	+2.0%
fps	610.21ms	604.28ms	-1.0%
lazysegtree	2.471s	1.742s	-29.5% ✅
maxflow	773.55ms	769.44ms	-0.5%
mincostflow	45.17ms	46.30ms	+2.5%
prime_fact	2.020s	2.034s	+0.7%
scc	319.36ms	319.48ms	+0.0%
segtree	746.26ms	610.49ms	-18.2% ✅
two_sat	1.303s	1.289s	-1.1% ✅

💾 Peak memory (lower is better)

Benchmark	Base	PR	Delta
acl_math	4.9KiB	4.9KiB	+0.0%
acl_string	13.5MiB	13.5MiB	+0.0%
convolution	16.1MiB	16.1MiB	+0.0%
dsu	40.4MiB	40.4MiB	+0.0%
fenwicktree	8.9MiB	8.9MiB	+0.0%
fps	3.9MiB	3.9MiB	+0.0%
lazysegtree	9.8MiB	9.8MiB	+0.0%
maxflow	97.0MiB	97.0MiB	+0.0%
mincostflow	16.3MiB	16.3MiB	+0.0%
prime_fact	8.5KiB	8.5KiB	+0.0%
scc	25.1MiB	25.1MiB	+0.0%
segtree	6.0MiB	6.0MiB	+0.0%
two_sat	174.0MiB	174.0MiB	+0.0%

_{Base = target branch, PR = this branch. Negative delta = improvement. ✅ improvement ≥ 1%, ⚠️ regression > 5%. "n/a" base entries mean the target branch has no benchmark suite yet.}